Being as my left eye is dominant and I normally shoot a handgun right handed, my dominant eye would be perfectly lined up shooting weak hand.
When shooting RH(normal) I turn my head several degrees to the right to bring my left(dominant)eye inline with the gun ..So dominant eye either way.

__________________“The vulcan neck pinch is not half as powerful as the vulcan groin kick, but it's more politically correct”
~ spock

Learn to shoot from hip (or 'retention position'), 3/4 hip (see faribairn and sykes), or full extended AND any position in between. Use a "threat focused" sighting method.

There has been much research and actual gunfights showing a "meat and metal" method working at reasonable distances. Front sight only works in some ranges/situations.

In short if you are shooting to save your life, speed is life. Practice until you are confident of the minimum sighting required to make hits at various distances. For me, up to about 10 yards I will not even attempt to use my rear sight. under 5-7 yards I won't even wait to get my gun up to my sight plane.

Under about 3 yards I will shoot as soon as my gun is pointing at my target even if it is just a few inches above my holster.

Even past ten yards if there is limited possibility of overpenetration or unintended targets I will start firing as soon as I see the profile of my pistol in line with my target.

AND I am MOVING fast. bullets going toward the target and my movement tend to make my survival more likely.

So in short; PRACTICE (airsoft is fine for this if ammo is too expensive for live fire, but do live fire to verify that what you are doing with the airsoft will work). Good luck learning.

By the way, there are various body index/point shooting techniques that work with long arms as well (research Quick Kill) and these can be extended even to 75 or 100 yards with the help of a quality red dot or holographic sight and lots of practice.

About the only time I close one eye is if I am using a telescopic sight.

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